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Transforming Mathematical Models Using Declarative Reformulation Rules

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Learning and Intelligent Optimization (LION 2011)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6683))

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Abstract

Reformulation is one of the most useful and widespread activities in mathematical modeling, in that finding a “good” formulation is a fundamental step in being able so solve a given problem. Currently, this is almost exclusively a human activity, with next to no support from modeling and solution tools. In this paper we show how the reformulation system defined in [13] allows to automatize the task of exploring the formulation space of a problem, using a specific example (the Hyperplane Clustering Problem). This nonlinear problem admits a large number of both linear and nonlinear formulations, which can all be generated by defining a relatively small set of general Atomic Reformulation Rules (ARR). These rules are not problem-specific, and could be used to reformulate many other problems, thus showing that a general-purpose reformulation system based on the ideas developed in [13] could be feasible.

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Author information

Authors and Affiliations

  1. Dipartimento di Informatica, Università di Pisa, Polo Universitario della Spezia, Via dei Colli 90, 19121, La Spezia, Italy

    Antonio Frangioni

  2. Dipartimento di Informatica, Università di Pisa, Largo B. Pontecorvo 3, 56127, Pisa, Italy

    Luis Perez Sanchez

Authors
  1. Antonio Frangioni
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  2. Luis Perez Sanchez
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Editors and Affiliations

  1. Departmento de Computation, Centro de Investigacion y de Estudios, Avanzados del Instituto Politecnico Nacional (CINVESTAV-IPN), Av. IPN No. 2508, Col. San Pedro Zacatenco, D.F. 0360, Mexico, Mexico

    Carlos A. Coello Coello

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Frangioni, A., Perez Sanchez, L. (2011). Transforming Mathematical Models Using Declarative Reformulation Rules. In: Coello, C.A.C. (eds) Learning and Intelligent Optimization. LION 2011. Lecture Notes in Computer Science, vol 6683. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-25566-3_30

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  • DOI: https://doi.org/10.1007/978-3-642-25566-3_30

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-25565-6

  • Online ISBN: 978-3-642-25566-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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